數學題!!!!***來:)

1.
10^(√3+1) • 100^(-√3/2)
= 10^(√3+1) • (10^2)^(-√3/2)
= 10^(√3+1) • 10^(-√3)
= 10^(√3+1-√3)
= 10^1
= 10


2.
[a^(1/√2)]^√2 • (b^√3)^√3
= a^[(1/√2)•√2] • b^(√3•√3)
= a^1 • b^3
= a b^3


3.
32^(-0.4) + 36^√5 • 81^0.75 • 6^(-√20)
= (2^5)^(-0.4) + (2^2•3^2) ^√5 • (3^4)^0.75 • (2•3)^(-2√5)
= 2^(-2) + 2^2√5 • 3^2√5 • 3^3 • 2^(-2√5) • 3^(-2√5)
= (1/2^2) + 2^(2√5 - 2√5) • 3^(2√5 + 3 - 2√5)
= 0.25 + 3^3
= 27.25


4.
(2 - √3)⁻³ + (2 + √3)⁻³
= [1 / (2 - √3)]³ + [1 / (2 + √3)]³
= [(2 + √3) / (2 - √3)(2 + √3)]³ + [(2 - √3) / (2 - √3)(2 +√3)]³
= [(2 + √3) / (2² - 3)]³ + [(2 - √3) / (2² - 3)]³
= (2 + √3)³ + (2 - √3)³
= (2)³ + 3(2)²(√3) + 3(2)(√3)² + (√3)³ + (2)³ - 3(2)²(√3) + 3(2)(√3)² - (√3)³
= 16 + 36
= 52


5.
[a^2 • (a^-3)^2]^-1
= [a^2 • a^-6]^-1
= [a^-4]^-1
= a^4


6.
(a^-2)^3 • a^4
= a^-6 • a^4
= a^-2
= 1/a^2


7.
(2^2 • 2^-1)^2 + (3^2 + 5^3)^0
= (2^1)^2 + 1
= (2^2) + 1
= 5


8.
(a^-3 - b^-3)(a^-3 + b^-3)
= (a^-3)^2 - (b^-3)^2
= a^-6 - b^-6
= (1/a^6) - (1/b^6)